Estimation of P(X>Y) for the Positive Exponential Family of Distributions

A positive exponential family of distributions is taken into consideration. Two measures of reliability are discussed. Uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are developed for the reliability functions. In addition to the UMVUES and MLES, we derive the method of moment estimators (MOME). The performances of two types of estimators are compared through Monte Carlo simulation